Turbulent flow over water waves in the presence of stratification

Direct numerical simulation is used to investigate stratified turbulent flow over a series of prescribed moving water waves at a bulk Reynolds number Re=8000 and waveslope ak=0.1. Unstable, neutral, and stable stratifications are considered for a range of wave phase speeds c. Stratification is shown to significantly alter the mean vertical profiles of velocity and temperature, turbulence variances, wave-induced flow fields, and surface form stress. For the range of conditions considered, the surface form stress (drag) and flow patterns (critical-layer height and streamlines) are well correlated with the friction velocity u*, which therefore contains the essential information about stratification influences. Nonseparated sheltering [Belcher and Hunt, Annu. Rev. Fluid. Mech. 30, 507 (1998)], which determines the drag in neutral flow over stationary topography, is modified by stratification and the movement of the underlying waves. The variation of the form stress with phase speed is correlated with the movement of the critical layer above the surface. Compared to neutral flow at a given phase speed, the flow patterns with unstable stratification are similar to the flow patterns over slower moving waves while stable stratification results in flow patterns typical of faster moving waves. This behavior is qualitatively captured by the wave age parameter c/u*. The wave-induced temperature field responds to the wave-induced velocity fields by forming positive and negative patches over the wave crests and troughs, respectively, with the resulting wave-induced heat flux as much as 15% of the total surface heat flux. Estimates of wave growth from the DNS are in reasonable agreement with field observations and laboratory experiments, and they are larger than predictions from high Reynolds-number, second-order closure models for c/u* 10, the present calculations predict less negative form stress (or less damping) of the waves compared to second-order closure models.